Brief Announcement: Rapid Mixing of Local Dynamics on Graphs

Authors Laurent Massoulié, Rémi Varloot

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Laurent Massoulié
Rémi Varloot

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Laurent Massoulié and Rémi Varloot. Brief Announcement: Rapid Mixing of Local Dynamics on Graphs. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 59:1-59:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


In peer-to-peer networks, it is desirable that the logical topology of connections between the constituting nodes make a well-connected graph, i.e., a graph with low diameter and high expansion. At the same time, this graph should evolve only through local modifications. These requirements prompt the following question: are there local graph dynamics that i) create a well-connected graph in equilibrium, and ii) converge rapidly to this equilibrium? In this paper we provide an affirmative answer by exhibiting a local graph dynamic that mixes provably fast. Specifically, for a graph on N nodes, mixing has occurred after each node has performed O(polylog(N)) operations. This is in contrast with previous results, which required at least Omega(N polylog(N)) operations per node before the graph had properly mixed.
  • Markov chains
  • Mixing time
  • Dynamic graphs
  • Local dynamics


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